Nitrogen is in the second row with no $d$ orbital in the valence shell. It obeys the octet rule and cannot have more than 8 electron.
There are exceptions to the octet rule. Having less than 8 electron is less preferable but still possible, and is commonly seen in free radicals and cations. On the other hand, having more than 8 electron is extremely unfavorable for second period atoms. Such electronic structures can be found in extremely unstable species or excited states, such as the CH5 radical.
As a comparison, first shell atoms obey the duet rule while atoms in the 3rd shell and beyond may obey 18-electron rule, 12-electron rule or 8-electron rule. However, 18-electron rule and 12-electron rules are much less strict than 8-electron rule and violations are common place.
According to valence bond theory, the electronic structure of a molecule is a combination of all possible resonance structure that you can write down, including structures with all possible formal charges and strange electron counts. However, their contributions are not even. some of them are more favorable than others.
For HNO3, in order to satisfy the octet rule, the nitrogen atom would form 1 double bond and 2 single bonds. Based on octet rule alone, there are 3 possible resonance structures that are favorable.
However, the first two resonance structures are significantly more favorable than the third, because they have smaller amount of formal charges. As a result, we usually only write the two dominant structures. The bond between OH and N is close to a normal single bond. The other two N-O bonds have bond order near 1.5.
It is also common to write a mixture of resonance structures as the hybrid form
Note that this representation is not a single Lewis structure, but a convenient way to represent many resonance structures in the same figure. It gives no information about the exact bond order or formal charges on individual atoms. The dotted lines indicates that in some structures where that bond is a single bond and in others a double bond, and the order is somewhere between 1 and 2.